Program Structureteacher.scholastic.com/products/dothemath//pdfs/DTMN... · 2020-04-20 · 4 Write a multiplication equation for the equal groups. The rectangles below are constructed

xii Introduction

Teach a total of fifteen lessons by repeating steps 2 through 4.

Program Structure

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multiplication & division 1

Unit 1: Beginning-of-Unit Assessment

1 4 4 4 4 4 4

2 6 6 6

3 Write a multiplication equation for 3 3 3 3 3 15.

4 Write a multiplication equation for the equal groups.

�The rectangles below are constructed with square tiles. Write a multiplication equation for each one that shows the total number of square tiles in each rectangle.

5

6

7

8

9 3 6

10 4 4

11 5 1

12 4 5

�Do your best at solving the problems below. Don’t worry if you have difficulty—your answers will tell your teacher about what you know and what you need to learn.

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1multiplication & division

13 6 3

14 5 6

15 0 11

16 3 0

17 10 8

18 7 10

19 Write a multiplication equation to solve.

There are 6 dogs. Each dog has 2 ears. How many ears are there in all?


There are 5 cars. Each has 4 tires. How many tires are there in all?

21 Write a word problem based on the equation below.

3 4 12

22 Write a multiplication problem for the addition problem below. Explain how you know your answer is correct.

2 2 2 2 2


Lesson 2Lesson 1PLANNER Lesson AssessLesson 4Lesson 3

Lessons 1–5

5

UNIT

1

Lesson Summary Students brainstorm things that come in equal groups of twos, threes, fours, fives, and sixes.

Students write and solve equations for multiplication word problems.

Students write and solve multiplication word problems for a given equation.

Students compare two word problems with the same factors in reverse order, learning that reversing the order of the factors produces different word problems with the same answer.

Students demonstrate understanding of the objectives of Lessons 1–4 by completing WorkSpace pages independently.

Objectives Identify examples of equal groups. • Communicate ideas with key math •vocabulary: equal.

Calculate products with factors 1 through 6.•

Write an equation for a multiplication •word problem.

Communicate ideas with key •math vocabulary: equal, equation, multiplication, and times.

Write a multiplication word problem •for a given equation.

Calculate products with factors •1 through 6.

Introduce key math vocabulary: •equal, equation, multiplication, and times.






Write an equation for a multiplication •word problem.


Communicate ideas with key math •vocabulary: equal and multiplication.

Materials S Student Bag

Unit 1: Beginning-of-Unit Assessment

WorkSpace • pages 3 and 4chart paper•

WorkSpace• pages 5 and 6 Things that come in groups • charts from Lesson 1

WorkSpace• pages 7, 8, 190 and 195–198 • Things that come in groups charts from Lesson 1chart paper •blank paper •

WorkSpace• pages 9 and 10 • Things that come in groups charts from Lesson 1 chart paper • from Lesson 3

•WorkSpace pages 11–15 • Things that come in groups charts from Lesson 1Circles and Stars Capture• cards Additional Practice•

Built-in Differentiation

Writing the names of items that come in groups of given amounts contributes to students’ vocabulary development.

Using symbolic representations of students’ figuring allows all students to follow different methods of reaching a solution.

Writing equations on the board and then reading them aloud reinforces the language of mathematics.

Solving problems presented using a graphic organizer gives students introduction to reversing factors in a multiplication problem following a familiar routine.

Assessing understanding through problems presented in a familiar graphic organizer allows students to show their understanding without having to approach the material in an unfamiliar context.

Interactive Whiteboard Toolscontains all hands-on manipulatives and WorkSpace pages for Unit 1, Lessons 1–5.

TeacherSpace CD-ROM contains Unit Assessments, Additional Practice pages, and other reproducibles to support teaching these lessons.

Understanding the M

eaning of M

ultiplication

2 Build a Foundation for Multiplication

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Understanding the M

eaning of M

ultiplication

Lessons 1–5

UNIT

1

FROM MaRilyn BuRns

Dear Colleague,The lessons that begin this unit develop and reinforce students’ understanding by connecting multiplication to real-world contexts. Lesson 1 begins by engaging students in brainstorming things that come in equal groups. Students first focus on things that come in equal groups of 3s—legs on stools, sides on triangles, triplets, and so on. They then expand their thinking to things that come in equal groups of 2s, 4s, 5s, and 6s.

Things that come in groups of 4

wheels on a carlegs on a tablesides on a square

Then, in Lessons 2 through 5, students write and solve multiplication word problems. Writing multiplication word problems helps reinforce for students the essential idea that defines multiplication situations—combining equal groups. We’ve found that having students write their own problems helps cement their understanding of multiplication and increases their success with solving word problems.

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The Teacher Guide is organized into five units of fifteen lessons each.

Every fifth lesson is an assessment that provides an opportunity to monitor student progress. Beginning-of-Unit and End-of-Unit Assessments measure student understanding.

2

Beginning-of-Unit AssessmentStudents complete the assessment as a pre-unit snapshot of what they know (see pages 341 and 342 for an example).

Prepare The Unit Overview offers a summary of the content and instruction of the following fifteen lessons. Planners are provided before each set of five lessons, as is a letter from Marilyn Burns explaining the context and goals of the upcoming lessons.

1

UN

IT 1

CONTENTS

Build a Foundation for MultiplicationAlthough students may have previous experience with multiplication, we take a step back in this unit and deepen students’ conceptual understanding of the meaning of multiplication by drawing on real-world contexts and rectangular arrays. Playing Multiplication Bingo engages students’ interest while giving them practice with multiplication facts.

Students will…• Use visual models to represent multiplication of whole numbers.

• Calculate products for factors 0, 1–6, and 10.

• Write and solve multiplication word problems.

• Communicate ideas with key math vocabulary: equal, equation, factor, multiplication, multiply, product, and times.

LESSONS 1–5

Understanding the meaningof multiplication . . . . . . . . . . . . . 1–22Identifying everyday objects that come in equal groups . . . . . . . . . . . . . .4

Solving problems with equal groups. . . .8

Writing and solving word problems. . . .12

Comparing equations for word problems . . . . . . . . . . . . . . . . . . . . . . . 16

Assessing student understanding. . . . . 20

LESSONS 6–10

Practicing multiplicationfacts . . . . . . . . . . . . . . . . . . . . . . . . . . . .23–44Calculating problems with factors 1 through 6 . . . . . . . . . . . . . . . . . . . 26

Practicing facts with Multiplication Bingo. . . . . . . . . . . . . . . . . . . 30

Calculating products when one factor is zero. . . . . . . . . . . . . . . . . . . . . . . . . . 34

Multiplying with 10 as a factor . . . . . . . 38


LESSONS 11–15

Connecting multiplication to arrays, rectangles, and the multiplication chart . . . . . . . 45–66Writing multiplication equations for equal rows . . . . . . . . . . . . . . . . . . . . . . . . 48

Relating equal rows of tiles to multiplication. . . . . . . . . . . . . . . . . . . . . . .52

Practicing facts with Tiles Capture . . . . 56

Relating rectanglesto multiplication. . . . . . . . . . . . . . . . . . . . . . 60


Measuring StudentUnderstanding With theEnd-of-Unit Assessment . . . . . . . . . . . 67

UNIT

1Lessons 1–15

Tiles Capture

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xiii

Each unit follows the same progression of steps 1 through 5.

Lesson SummaryStudents brainstorm things that come in equal groups of twos, threes, fours, fives, and sixes.

AssessAdminister the Unit 1: Beginning-of-Unit Assessment before beginning today’s instruction.

ObjectivesIdentify examples of equal groups. •Communicate ideas with key math •vocabulary: equal.

MaterialsWorkSpace• pages 3 and 4chart paper•

Interactive Whiteboard Tools

WorkSpace pages and manipulatives for Lesson 1 are provided on the Interactive Whiteboard Tools CD-ROM.

PreparationUnit 1: Beginning-of-Unit AssessmentMake 1 copy of the assessment for each student from pages 341–342 or the TeacherSpace CD-ROM.

Language DevelopmentKey Math VocabularyENGLISH SPANISH

equal igual

Academic VocabularyENGLISH SPANISH

car auto

finger dedo

group grupo

insect insecto

stool banquete

wheel rueda

LessonLesson


Lesson 1 Students brainstorm things that come in equal groups.

Next Lesson Students write and solve equations for multiplication word problems.

Guide students to brainstorm things that come in groups of 2.

1 Introduce the lesson.h It always helps to connect ideas to real-world examples

when learning math. Here we’re going to focus on the basic idea of multiplication by thinking about things in the world that come in equal groups. I’ll start us with some simple examples and then you’ll come up with your own examples.

2 List things that come in groups of 2.Post a piece of chart paper and write on it as shown.


ears

Ask a student to read the title.

h Who can explain why I wrote ears on this chart paper? (People have 2 ears.)

What other things can we write on the list?

List students’ suggestions. (Possibilities include shoes, chopsticks, legs, feet, hands, etc.)

3 Students write the list.Have students turn to WorkSpace page 3.Choose a student to read the list and then have students list additional things that come in twos from the chart paper.

Guide students to brainstorm things that come in groups of 3.

1 List things that come in groups of 3.h I wouldn’t write legs on a stool on our list of

things that come in twos. Who can explain why?

Ask a student to explain.

h On what list does legs on a stool belong? (Things that come in groups of 3)

Post a piece of chart paper and write on it as shown.


legs on a stool


h What other things can we write on the list?

List students’ suggestions. (Possibilities include wheels on a tricycle, colors on a traffic light, legs on a tripod, etc.)

2 Students write this list on WorkSpace page 3.Have a student read the things listed for groups of 3 on page 3. Then have them list additional things from the chart paper.

Language DeveLopmentSome of the words on the Things that come in groups lists may be unfamiliar to your students. This activity is a great way to build vocabulary; just knowing that bicycles have two wheels and tricycles have three is helpful. Also, it may help to show pictures. You might also draw a simple sketch of items on the list.

Students brainstorm things that come in groups of 4.

1 List things that come in groups of 4.h What about wheels on a car? On what list does

wheels on a car belong? (Things that come in groups of 4)



wheels on a car


h What other things can we add to the list?

List students’ suggestions. (Possibilities include legs on a chair, edges of a picture frame, legs on a cow, etc.)

2 Students write this list on WorkSpace page 4.Have a student read the things listed for groups of 4 on page 4. Then have them list additional things from the chart paper.

whoLe group whoLe group

1Step 2Step 3StepIdentifying everyday objects that come in equal groups1

whoLe group

Things That Come in Groups

Workspace page 3 Things That Come in Groups

Workspace page 4

Continue

5UNIT 1 Lesson 1

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4Step Students brainstorm things that come in groups of 5 and 6.1 List things that come in groups of 5.h What about fingers on a hand? On what list does

fingers on a hand belong? (Things that come in groups of 5)



fingers on a hand


h What other things can we add to our list?

Have students think, pair, share. (Possibilities include toes on a foot, petals on a violet, sides on a pentagon, etc.)

2 List things that come in groups of 6.Follow the same procedure as for groups of 2, 3, 4, and 5.

3 Students write lists for 5 and 6 on WorkSpace page 4.

SUPPORTING INSTRUCTIONThink, pair, share is a routine that will be used throughout this program. Having students talk in pairs provides them a “safe” way to share ideas that they may not be quite sure of, think of words to articulate their ideas, brainstorm, and practice what they will say when they share with the larger group.

Explain the routine to students: they think first and then share their thoughts with their partners, take turns listening and speaking, and finally discuss what they will say when they share with the whole group.

Partners brainstorm things that come in equal groups.

1 Students work in pairs to complete WorkSpace pages 3 and 4.Have students work together to add more items to the lists on pages 3 and 4.


Groups of 2 Groups of 3

WORkSPaCe PaGe 3


Groups of 5Groups of 4

Groups of 6

WORkSPaCe PaGe 4

Students share items they added to their lists.

1 Choose a pair to report one item they added to a list.Leave about five minutes before the end of class for students to report examples from their Things that come in groups lists. As the pair you chose reports the item, write it on the appropriate chart and have students write it on the corresponding list in their WorkSpaces.

2 Have other pairs report their items for the rest of the available time.

SUPPORTING INSTRUCTIONKeep the class charts posted; students will use them when they write and solve word problems in Lessons 2–5.

Step5 Step6whole group partners whole group

1 Identifying everyday objects that come in equal groupslessoncontinued

Stop

6 Build a Foundation for Multiplication 7UNIT 1 Lesson 1

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Assessing student understandingcontinued

Lesson

additionaL practice

CheckPoint

55

All students could benefit from additional practice. For your convenience, the reproducible of the Additional Practice for Lessons 1–5 is available on the TeacherSpace CD-ROM. This Additional Practice gives students more opportunities to write and solve equations for multiplication word problems.

For Students Ready for a Challenge

Some students may like the challenge of greater •numbers as it makes them feel good about their ability to solve “hard” problems. If a student is constantly choosing very easy numbers, it is most likely that those are the numbers he or she is most comfortable using; however, some students may not have thought to choose greater numbers. If you think a particular student needs a challenge, pose a problem such as: There are 6 scorpions. Each scorpion has 8 legs. How many legs are there in all?

For Students Who Need More Support

Ask the student if he or she prefers to draw •pictures, use numbers, or use words to show how he or she figured a problem. Then model a solution to a word problem using the student’s preferred method. This will help him or her feel more comfortable and solve the problem with more confidence.

Play • Circles and Stars Capture one-on-one with the student. This allows you to guide the student through figuring the total number of stars without counting them, while reinforcing the language of multiplication. For example:

There are 3 groups with 2 stars in each –circle.

There are 3 equal groups of 2 stars.–

3 groups of 2 equals 6.–

3 times 2 equals 6.–

Have the student play a solitaire version of •Circles and Stars Capture. The student turns over two cards, figures the total for each, and decides which has the greater number of stars. Encourage the student to record an equation for each card and draw a star next to the one with the greater product.

Monitor Progress and Differentiate InstructionUse the Annotated WorkSpace to assess pages 11 and 12. Although these lessons are carefully paced and scaffolded, there may be instances when students need additional support or challenges.


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multiplication & division 1

Name: Date:

Unit 1: End-of-Unit Assessment

1 3 3 3 3 3 3

2 5 5 5

3 Write a multiplication equation for 4 4 4 4 4 20.

4 Write a multiplication equation for the equal groups.

�The rectangles below are constructed with square tiles. Write a multiplication equation for each one that shows the total number of square tiles in each rectangle.

5

6

7

8


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1

9 2 6

10 3 3

11 6 1

12 3 4

13 5 2

14 6 5

15 0 9

16 5 0

17 12 10

18 10 9


There are 4 cats. Each cat has 2 ears. How many ears are there in all?


There are 5 salads. Each has 3 tomatoes. How many tomatoes are there in all?

21 Write a word problem based on the equation below.

4 6 24

22 Write a multiplication problem for the addition problem below. Explain how you know your answer is correct.

2 2 2 2 2 2

multiplication & division


3 5 4

Teach the LessonsEach lesson begins with a sidebar containing the Lesson Summary, Objectives, Materials, Interactive Whiteboard Tools, Preparation, and Language Development, followed by step-by-step instruction.

Assess Student UnderstandingEvery fifth lesson is an opportunity to monitor student progress with Show What You Know WorkSpace pages. The CheckPoint page provides ideas for differentiating instruction and offers additional practice.

End-of-Unit AssessmentThis assessment measures student growth when compared with the results of the Beginning-of-Unit Assessment. Use the Objectives Tracker (see page 339 for an example) to record student achievement for each unit.

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Program Structureteacher.scholastic.com/products/dothemath//pdfs/DTMN... · 2020-04-20 · 4 Write a multiplication equation for the equal groups. The rectangles below are constructed